The answer to your question is hidden in the library (description of mechanics and tips) and in alchemy.
The game assumes that the player will help Celica actively learn and improve skills (alchemy, learning to do without artifacts on the neck).
As for the cyclops and some other tricky monsters, the game hopes that the player will remember about potions (alchemy). Celica drinks a potion before the battle and she gains immunity. The purpose of immunity depends on the potion you prepared. In addition, the better Celica has mastered the skills, the easier it is for her to defeat monsters.
In general, visit the library :-)